Examine the diagram at right.  

1. Are the triangles in this diagram similar? If they are, use a flowchart with justifications or a two-column proof to prove similarity. If they are not similar, explain why not. Explain.

   Hint (a):

   Do the marks help prove they are similar? If so, how? What makes these triangles similar? Are there any angles that are congruent?

   Partial Answer (a):

   Yes, by $\text{SAS}\sim$ because Segment $FI$ is proportional to segment $FG$, $∠F≅∠F$, and segment $FJ$ is proportional to segment $FH$.

2. Name all the pairs of congruent angles in this diagram you can.

   Hint (b):

   Look at the triangles, what angles are corresponding to each other?

3. Are $\overline{GH}$ and $\overline{IJ}$ parallel? Explain how you know.

   Hint (c):

   How can knowing sets of congruent angles, help you prove the sides are parallel?

   Answer (c):

   Yes they are parallel, because corresponding angles are congruent.

4. If $GH=4x-3$ and $IJ=3x+14$, find $x$. Then find the length of $\overline{GH}$.

   Hint (d):

   How are the lengths of $\overline{GH}$ and $\overline{IJ}$ related? How will this help you solve for $x$?